Engineering

You will not only need JEE Mains marks, but need an excellent JEE score, and in addition to that you also need an excellent percentage in 12th standard so as to get the name in the cutoff list of DTU.

Actually no college is the worst, every college is have its own speciality. But if your looking for best colleges, so first of all it depends upon your marks, then based on that you get your college. Being best I would recommend for IIT or NIT first if you attain good marks in 12th and in entrance exam. If looking for best private colleges, so I would recommend you to go for LPU because of it's better in all aspects whether talks about teaching, infrastructure or placement cell. So I hope you get your answer.

Yes, you can do it, but according to my opinion it is actually not a good option to opt for psychology after B.Tech be honest to say about that thing.

Indian Institute of Technology Bombay, Institute of Chemical Technology
National Institute of Industrial Engineering and if you consider and search for Bhubaneswar
Gandhi Vihar Bhubaneswar. https://www.gec.edu.in/Department.php.